In wireless communication systems, channel state information (CSI) at the receiver is obtained through transmission of a number of known pilot or training symbols, and using an estimation algorithm at the receiver to estimate the unknown channel based on the knowledge of the transmitted symbols. The estimation variance depends on the noise variance, number of the channel components to be estimated, and number of the pilot or training symbols (number of independent measurements). However, in general, the more the number of channel measurements, the lower the estimation variance will be. For a slowly fading channel where the fading coefficients remain approximately constant for many symbol intervals, the transmitter can send a large number of training or pilot symbols per channel realization without a significant loss in the data rate, and allow the receiver to accurately estimate the fading coefficients. In this case, one can safely use a perfect CSI assumption to design optimal codes and constellations.
In fast fading channels, however, this approach (sending a large number of training or pilot symbols) is either infeasible (due to the fast variations of the channel), or results in a significant loss in the actual data rate (due to the fraction of the time spent on training). Because of the increased number of channel parameters, this problem becomes even more acute in MISO (multiple input, single output) and MIMO (multiple input, multiple output) systems. As a result, in high mobility environments, the number of measurements per channel realization is relatively small and the estimation quality is affected by one or both of the following effects:                The number of measurements per channel component is very small, resulting in a larger estimation variance due to the additive noise,        Some of the channel components are not estimated at all (e.g., the paths with small energy in a multipath environment). These components appear as additive terms in the estimation variance, which do not vanish at high SNR and result in an error floor in the performance curves.        
In the presence of channel estimation errors due to the above effects, the code and constellations that are designed for the case of perfect CSI are no longer optimal.
Prior art approaches typically assume that the receiver has perfect channel state information, and the conventional constellations and multiple-antenna techniques (such as transmit diversity or BLAST™ scheme), which are designed for perfect CSI at the receiver were used. As a result, either very poor performance was achieved due to the estimation errors (especially in fast fading environments), or a large fraction of the system resources had to be used for training, resulting in a substantial reduction in the achievable rates.
What is needed in the art is a signal constellation specifically designed with the assumption of imperfect channel state information at the receiver that remains robust with fast-fading channels. Such as signal constellation would be particularly advantageous in a multi-path communication system, especially a system wherein the transmitter employs more than one transmit antenna (such as a MIMO OFDM or a MC-CDMA system). At least in such fast fading environments, such a signal constellation should offer performance improvement over conventional signal constellations that were designed with the assumption of perfect channels state information at the receiver, without increasing bandwidth or reducing data rates.